You seem to be talking about two different effects.
When an induction generator is grid connected, the grid sets the frequency. If the speed is more than 2% or 3% above the synchronous frequency or if the slip frequency is more than 2% or 3% above or below synchronous speed, the motor will overheat.
referring to the first ink you posted; Look at the bottom figure.
For grid connection refer to the vertical line shown as speed-100, slip-0
Now look at the point marked full load operating point and the point marked n
s.
Normal motoring operation is between these points.
A slip of 1 occurs only during the first moment of starting and under fault conditions. Sustained operation with a slip of 1 will result in motor destruction from excess heat in less than a minute.
Again, normal operation is with very low slip values.
Generating;
In the figure shown, generating is the area below the center base line. If synchronous speed is n
s Then motoring is n
s minus slip and generating is n
s plus slip. Slip in both cases is in the order of a few percent.
When the induction generator is islanded (running independently of the grid) the frequency is determined by the speed and by the slip.
Referring back to the figure posted in the link, when the induction generator is islanded the vertical line on the figure shown as speed 100 or n
s will shift with the driven speed, and the load frequency will be lower within a few percent of the synchronous frequency.
While the figure shows the range of -100 speed to +200 speed, (in percentage) and slip as -2 to +1 (in per unit) {confusing},
and while slip of 1 is important for brief periods during starting, safe sustained operation of either a motor or a generator is in the order of 97% speed to 103% speed or -0.03 to + 0.03 slip.
The "U" frame motors in common use 50 years ago were often "plugged" or reversed or stopped by the application of a reverse rotating magnetic field, basically throwing the motor into reverse while running at full speed forward.
Plugging when the way of the Dodo with the introduction of the "T" frame motors common today, with much shorter allowable locked rotor times.
Referring again to the figure, you will see that the torque in the region of -100 to 0 speed is less than the torque in the region from 0 speed to +100 speed. The time to slow the motor to a stop is greater than the time to accelerate the motor to full speed. As a result the heating of the motor may be several times as great during the deccelleration time as during the normal starting period.
Another effect to be aware of:
When a generator is grid connected, an increase in the driving torque results in the generator picking up more of the load from the other generators on the grid.
When a generator is islanded, an increase in the driving torque results in the generator frequency increasing.
Bill
--------------------
"Why not the best?"
Jimmy Carter